Abstract Uncertainty in logic programming has been widely investigated in the last decades, leading to multiple extensions of the classical logic programming paradigm. However, few of these are designed as extensions of the well-established and powerful Constraint Logic Programming (CLP) scheme for CLP. In a previous work we have proposed the proximity-based qualified constraint logic programming (SQCLP) scheme as a quite expressive extension of CLP with support for qualification values and proximity relations as generalizations of uncertainty values and similarity relations, respectively. In this paper we provide a transformation technique for transforming SQCLP programs and goals into semantically equivalent CLP programs and goals, and a practical Prolog-based implementation of some particularly useful instances of the SQCLP scheme. We also illustrate, by showing some simple – and working – examples, how the prototype can be effectively used as a tool for solving problems where qualification values and proximity relations play a key role. Intended use of SQCLP includes flexible information retrieval applications.

Abstract Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause annotations based on uncertain truth values, qualification values as a generalization of uncertain truth values, and unification based on proximity relations. On the other hand, the CLP scheme has established itself as a powerful extension of LP that supports efficient computation over specialized domains while keeping a clean declarative semantics. In this paper we propose a new scheme SQCLP designed as an extension of CLP that supports qualification values and proximity relations. We show that several previous proposals can be viewed as particular cases of the new scheme, obtained by partial instantiation. We present a declarative semantics for SQCLP that is based on observables, providing fixpoint and proof-theoretical characterizations of least program models as well as an implementation-independent notion of goal solutions.

Abstract This paper presents a computational model for the cooperation of constraint domains and an implementation for a particular case of practical importance. The computational model supports declarative programming with lazy and possibly higher-order functions, predicates, and the cooperation of different constraint domains equipped with their respective solvers, relying on a so-called constraint functional logic programming (CFLP) scheme. The implementation has been developed on top of theCFLPsystem , supporting the cooperation of the three domains ℋ, ℛ, and ℱ , which supply equality and disequality constraints over symbolic terms, arithmetic constraints over the real numbers, and finite domain constraints over the integers, respectively. The computational model has been proved sound and complete w.r.t. the declarative semantics provided by theCFLPscheme, while the implemented system has been tested with a set of benchmarks and shown to behave quite efficiently in comparison to the closest related approach we are aware of.

Similarity-based Logic Programming (briefly, SLP) has been proposed to enhance the LP paradigm with a kind of approximate reasoning which supports flexible information retrieval applications. This approach uses a fuzzy similarity relation ℝ between symbols in the program's signature, while keeping the syntax for program clauses as in classical LP. Another recent proposal is the QLP(D) scheme for Qualified Logic Programming, an extension of the LP paradigm which supports approximate reasoning and more. This approach uses annotated program clauses and a parametrically given domain D whose elements qualify logical assertions by measuring their closeness to various users' expectations. In this paper we propose a more expressive scheme SQLP(ℝ, D) which subsumes both SLP and QLP(D) as particular cases. We also show that SQLP(ℝ, D) programs can be transformed into semantically equivalent QLP(D) programs. As a consequence, existing QLP(D) implementations can be used to give efficient support for similarity-based reasoning

This paper presents a computational model for the cooperation of constraint domains, based on a generic Constraint Functional Logic Programming (CFLP) Scheme and designed to support declarative programming with functions, predicates and the cooperation of different constraint domains equipped with their respective solvers. We have developed an implementation in the CFLP system TOY, supporting an instance of the scheme which enables the cooperation of symbolic Herbrand constraints, finite domain integer constraints, and real arithmetic constraints. We provide a theoretical result and an analysis of benchmarks showing a good performance with respect to the closest related approach we are aware of

The new generic scheme CFLP (D) has been recently proposed in [24] as a logical and semantic framework for lazy constraint functional logic programming over a parametrically given constraint domain D. In this paper we extend such framework with a suitable operational semantics, which relies on a new constrained lazy narrowing calculus for goal solving parameterized by a constraint solver over the given domain D. This new calculus is sound and strongly complete w.r.t. the declarative semantics of CFLP (D)programs, which was formalized in [24] by means of a Constraint Rewriting Logic CRWL (D).

Constraint Logic Programming (CLP) and Hereditary Harrop formulas (HH) are two well known ways to enhance the expressivity of Horn clauses. In this paper, we present a novel combination of these two approaches. We show how to enrich the syntax and proof theory of HH with the help of a given constraint system, in such a way that the key property of HH as a logic programming language (namely, the existence of uniform proofs) is preserved. We also present a procedure for goal solving, showing its soundness and completeness for computing answer constraints. As a consequence of this result, we obtain a new strong completeness theorem for CLP that avoids the need to build disjunctions of computed answers, as well as a more abstract formulation of a known completeness theorem for HH.